The KP hierarchy is one of the most important integrable hierarchies and it arises in many different fields of mathematics and physics such as enumerative algebraic geometry, topological field and string theory[1]}, [2]}. Meanwhile Young diagrams and symmetric functions are of interest to
many researchers and have many applications in mathematics including combinatorics
and representation theory of the symmetric and general linear group[3]}, [4]}, [5]}, [6]}. Schur functions can be used to describe the tau functions of the KP hierarchy, and the vertex operators which realize the Schur functions have close relations with the Fermions in the KP hierarchy. In this paper, we generalize these to the case of Jack polynomials and \(\hbar \) -KP hierarchy.
